Apparatus for decoding quasi-orthogonal space-time block codes

ABSTRACT

An efficient decoding scheme of a receiver in a wireless communication system including a transmitter for encoding data into quasi-orthogonal space-time block codes (STBCs) and transmitting the STBCs through a plurality of transmit antennas using fading channels, and a receiver for receiving data through a plurality of receive antennas. In the decoding scheme, channel matched filtering is performed on M N-dimensional equivalent reception vectors {right arrow over (y)} m  received through M receive antennas and N-dimensional channel matched filtered vectors {right arrow over (y)} m,mat  are outputted. P L-dimensional sub-channel matched filtered vectors {right arrow over (y)} m,mat   i  are generated from each of the N-dimensional channel matched filtered vectors {right arrow over (y)} m,mat . P L-dimensional sub-equivalent channel matched filtered vectors {right arrow over (y)} m,mat   i  are generated using the sub-channel matched filtered vectors {right arrow over (y)} m,mat   i . Iterative interference cancellation and maximum likelihood (ML) decoding are performed on each of the L-dimensional sub-equivalent channel matched filtered vectors {right arrow over (y)} mat   i , and P L-dimensional sub-input vectors {right arrow over (x)} i  are demodulated.

PRIORITY

This application claims priority under 35 U.S.C. §119 to an application entitled “Apparatus for Decoding Quasi-Orthogonal Space-Time Block Codes” filed in the Korean Intellectual Property Office on Mar. 14, 2005 and assigned Serial No. 2005-21008, the contents of which are incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention generally relates to a wireless communication system, and more particularly to an efficient decoding scheme of a receiver in a transmission system using multiple antennas and quasi-orthogonal space-time block coding.

2. Description of the Related Art

To improve performance of a mobile communication system in a fading channel environment, a large amount of research is being conducted on a transmit antenna diversity scheme for transmitting data using multiple antennas.

Because the transmit antenna diversity scheme can obtain a diversity gain using a plurality of transmit antennas, it is a scheme suitable for the next generation high-speed data communication system.

To obtain an optimum transmit antenna diversity gain, space-time block codes (STBCs) with orthogonal characteristics based on an orthogonal design theory have been proposed. These STBCs have a maximum diversity order, and have an advantage in that maximum likelihood (ML) decoding can be performed in a receiving stage through a simple linear process.

However, when full rate orthogonal STBCs without using any additional frequency band employ a quadrature amplitude modulation (QAM) scheme, the maximum number of transmit antennas is only two.

When the number of transmit antennas is greater than two and STBCs do not have a special structure such as orthogonality in the QAM scheme, ML decoding complexity exponentially increases to Q^(N), where the modulation order is Q and the number of transmit antennas is N.

STBCs using quasi-orthogonal characteristics have been proposed which can obtain the maximum diversity gain without using any additional frequency band in the case where the QAM scheme is used even when the number of transmit antennas is greater than two.

Even though the ML decoding complexity of quasi-orthogonal STBCs exponentially increases to Q^(N/2), where the modulation order is Q and the number of transmit antennas is N, it is still low as compared with the ML decoding complexity of STBCs that do not have quasi-orthogonal characteristics.

Because the ML decoding complexity even in case of quasi-orthogonal STBCs exponentially increases in proportion to the number of transmit antennas, the ML decoding complexity becomes very high when the number of transmit antennas is greater than four or when a high modulation order is used.

To reduce the decoding complexity of quasi-orthogonal STBCs, suboptimal decoding schemes have been proposed which use a decorrelator, a minimum mean square error (MMSE) filter, or a successive interference canceller. However, because these decoding schemes do not obtain a diversity gain through the ML decoding method for given quasi-orthogonal STBCs, they have severe performance loss as compared with the ML decoding.

SUMMARY OF THE INVENTION

It is, therefore, an aspect of the present invention to provide a new suboptimal decoding apparatus that can fundamentally reduce the decoding complexity of quasi-orthogonal space-time block codes (STBCs).

It is another aspect of the present invention to provide a new suboptimal decoding apparatus that can fundamentally reduce the decoding complexity of quasi-orthogonal space-time block codes (STBCs) as compared with an ML decoding method, without a sudden performance loss by combining interference cancellation and maximum likelihood (ML) decoding in a suboptimal decoding method.

To achieve the above and other aspects of the present invention, a suboptimal decoding apparatus includes a plurality of channel matched filters for performing channel matched filtering on M N-dimensional equivalent reception vectors {right arrow over (y)}_(m) (m=1, . . . , M) received through M receive antennas under a fading channel environment and outputting N-dimensional channel matched filtered vectors {right arrow over (y)}_(m,mat) (m=1, . . . ,M); a plurality of grouping units for generating P L-dimensional sub-channel matched filtered vectors {right arrow over (y)}_(m,mat) ^(i) (i=1, . . . ,P, m=1, . . . ,M) from each of the N-dimensional channel matched filtered vectors {right arrow over (y)}_(m,mat); a combiner for generating P L-dimensional sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i) (i=1, . . . ,P) using the sub-channel matched filtered vectors {right arrow over (y)}_(m,mat) ^(i); and an interference cancellation decoder for performing iterative interference cancellation and maximum likelihood (ML) decoding on each of the L-dimensional sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat), and demodulating P L-dimensional sub-input vectors {right arrow over (x)}^(i) (i=1, . . . ,P).

Each of the plurality of grouping units includes a first extraction module for extracting signals from each of the channel matched filtered vectors {right arrow over (y)}_(m,mat) output by the channel matched filters in a unit of L signals such that the signals do not overlap with each other; and a plurality of grouping modules for grouping the L signals extracted from the first extraction module and generating the P L-dimensional sub-channel matched filtered vectors {right arrow over (y)}_(m,mat) ^(i).

The combiner includes a plurality of second extraction modules for extracting vectors from the P sub-channel matched filtered vectors {right arrow over (y)}_(m,mat) ^(i) outputted by each of the plurality of grouping units one by one; and a plurality of combination modules for combining M vectors extracted from the plurality of second extraction modules and generating the P L-dimensional sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i).

The interference cancellation decoder includes an interference canceller for performing iterative interference cancellation on each of the sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i) I times and generating K_(I) different estimation candidate vectors {right arrow over (x)}_(k) _(I) ^(i,(I)) (i=1, . . . ,P) for the L-dimensional sub-input vectors {right arrow over (x)}^(i); and an ML decoder for performing ML decoding on the estimation candidate vectors {right arrow over (x)}_(k) _(I) ^(i,(I)) and demodulating the P L-dimensional sub-input vectors {right arrow over (x)}^(i).

The decoding apparatus performs channel matched filtering on M N-dimensional equivalent reception vectors {right arrow over (y)}_(m) (m=1, . . . ,M) received through M receive antennas and outputting N-dimensional channel matched filtered vectors {right arrow over (y)}_(m,mat) (m=1, . . . ,M); generates P L-dimensional sub-channel matched filtered vectors {right arrow over (y)}_(m,mat) ^(i) (i=1, . . . ,P, m=1, . . . ,M) from each of the N-dimensional channel matched filtered vectors {right arrow over (y)}_(m,mat); generates P L-dimensional sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i) (i=1, . . . ,P) using the sub-channel matched filtered vectors {right arrow over (y)}_(m,mat) ^(i); and performs iterative interference cancellation and maximum likelihood (ML) decoding on each of the L-dimensional sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i), and demodulating P L-dimensional sub-input vectors {right arrow over (x)}^(i) (i=1, . . . ,P).

The sub-input vectors xi are demodulated from the sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i), respectively.

(L−1)-dimensional symbol vectors, from which a symbol x_(i) _(I) associated with one arbitrary element y_(mat,I) ^(i) within the sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i) is excluded, are defined as interference symbol vectors. The interference canceller eliminates interference from a plurality of initial interference symbol candidate vectors in one arbitrary element y_(mat,I) ^(i) within the sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i), and generates a plurality of signals from which the interference has been eliminated.

The interference canceller selects an arbitrary number of vectors, serving as candidate vectors of initial interference symbol vectors before performing the interference cancellation, from all (L−1)-dimensional symbol vectors from which a symbol x_(i) _(I) , associated with one arbitrary element y_(mat,I) ^(i) within the sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i), is excluded. For example, a method for determining the initial interference symbol vectors can select all Q^(L−1) vectors.

Alternatively, the interference canceller may select K₁ (K₁≦Q^(L−1)) arbitrary candidates of all Q^(L−1) candidates for the (L−1)-dimensional symbol vectors closest to the sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i) from the candidate vectors of the initial interference symbol vectors. However, the interference canceller may select only candidates present in a predetermined distance from the sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i) at

The interference canceller determines symbols x_(i) _(I) from the signals from which interference has been eliminated to generate the estimation candidate vectors, and combines values of the determined symbols x_(i) _(I) and the (L−1)-dimensional interference symbol vectors associated therewith.

The interference canceller performs iterative interference cancellation to reduce the number of estimation candidate vectors to be generated after eliminating interference from the sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i).

The estimation candidate vectors {right arrow over (x)}_(k) _(I) ^(i,(I)) are generated after iterative interference cancellation are performed on the sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i) I times.

The interference canceller selects new estimation candidate vectors by selecting only vectors that are different from the estimation candidate vectors generated after performing the interference cancellation in a method for determining the estimation candidate vectors after performing the interference cancellation.

The interference canceller performs iterative interference cancellation on the sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i) I times and determines K_(I) different estimation candidate vectors {right arrow over (x)}_(k) _(I) ^(i,(I)). As the iterative interference cancellation is performed, the number of different estimation candidate vectors is gradually reduced.

The ML decoder performs the ML decoding on the K_(I) estimation candidate vectors {right arrow over (x)}_(k) _(I) ^(i,(I)) generated from the interference canceller, and demodulates the L-dimensional sub-input vectors {right arrow over (x)}^(i).

When all Q^(L−1) symbol vectors are selected as candidates of initial interference symbol vectors in one example of an estimation candidate vector generating method, Q^(L−1) different estimation candidate vectors {right arrow over (x)}_(k) _(I) ^(i,(I)) are generated through one interference cancellation operation.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other aspects and advantages of the present invention will be more clearly understood from the following detailed description taken in conjunction with the accompanying drawings, in which:

FIG. 1 is a block diagram illustrating a decoding apparatus in accordance with a preferred embodiment of the present invention;

FIG. 2 is a block diagram illustrating details of a grouping unit of FIG. 1;

FIG. 3 is a block diagram illustrating details of a combiner of FIG. 1; and

FIG. 4 is a block diagram illustrating details of an interference cancellation decoder of FIG. 1.

DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

Preferred embodiments of the present invention will be described with reference to the accompanying drawings.

In a method for decoding quasi-orthogonal space-time block codes (STBCs) in accordance with the present invention, it is assumed that a wireless communication system includes N transmit antennas and M receive antennas, where M≧1 and N≧2.

FIG. 1 is a block diagram illustrating a decoding apparatus in accordance with a preferred embodiment of the present invention.

As illustrated in FIG. 1, the decoding apparatus includes a plurality of channel matched filters 20, a plurality of grouping units 30, a combiner 40, and an interference cancellation decoder 50. The channel matched filters 20 perform channel matched filtering on equivalent reception vectors {right arrow over (y)}_(m) (m=1, . . . ,M) and output N-dimensional channel matched filtered vectors {right arrow over (y)}_(m,mat) (m=1, . . . ,M The grouping units 30 generate P L-dimensional sub-channel matched filtered vectors {right arrow over (y)}_(m,mat) ^(i) (i=1, . . . ,P, m=1, . . . ,M) from the channel matched filtered vectors {right arrow over (y)}_(m,mat), respectively. The combiner 40 generates P L-dimensional sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i) (i=1, . . . ,P) using the sub-channel matched filtered vectors {right arrow over (y)}_(m,mat). The interference cancellation decoder 50 performs iterative interference cancellation and maximum likelihood (ML) decoding on each of the sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i) and demodulates P L-dimensional sub-input vectors {right arrow over (x)}^(i) (i=1, . . . ,P).

In quasi-orthogonal space-time block codes (STBCs), all elements of an N×N codeword matrix G({right arrow over (x)}) are complex linear combinations of N quadrature amplitude modulation (QAM) symbols x₁,x₂, . . . ,x_(N) within an input vector {right arrow over (x)} and their complex conjugate values x₁*,x₂*, . . . ,x_(N)*. The codeword matrix G({right arrow over (x)}) can be expressed as shown in Equation (1). $\begin{matrix} {{G\left( \overset{\rightarrow}{x} \right)} = {\sum\limits_{i = 1}^{N}{G_{i}\left( x_{i} \right)}}} & (1) \end{matrix}$

In Equation (1), G_(i)(x_(i)) denotes an N×N modulation matrix for symbols x_(i), where elements of G_(i)(x_(i)) are complex linear combinations of the symbols x_(i) and their complex conjugate values.

The codeword matrix G({right arrow over (x)}) can be decomposed as shown in Equation (2). $\begin{matrix} {{G\left( \overset{\rightarrow}{x} \right)} = {\sum\limits_{i = 1}^{P}{A_{i}\left( {\overset{\rightarrow}{x}}^{i} \right)}}} & (2) \end{matrix}$

In Equation (2), a matrix A_(i)({right arrow over (x)}^(i)) is a sum of modulation matrices G_(i) _(I) (x_(i) _(I) ), . . . , G_(i) _(L) (x_(i) _(L) ) associated with input symbols x_(i) ₁ , x_(i) ₂ , . . . , x_(i) _(L) , (i_(l)∈={1,2, . . . ,N}, l=1,2, . . . ,L) belonging to the i-th group when x₁,x₂, . . . , x_(N) are grouped into P (P=N/L) groups in a unit of L symbols such that they do not overlap with each other, and {right arrow over (x)}^(i)=[x_(i) _(I) , . . . , x_(i) _(L) ]^(T). That is, ${A_{i}\left( {\overset{\rightarrow}{x}}^{i} \right)} = {\sum\limits_{l = 1}^{L}{{G_{i_{l}}\left( x_{i_{l}} \right)}.}}$

In the quasi-orthogonal STBCs, the matrix A_(i)({right arrow over (x)}^(i)) can be selected such that Equation (3) is satisfied. $\begin{matrix} {{\sum\limits_{i < j}\left( {{{A_{i}\left( {\overset{\rightarrow}{x}}^{i} \right)}^{H}{A_{j}\left( {\overset{\rightarrow}{x}}^{j} \right)}} + {{A_{j}\left( {\overset{\rightarrow}{x}}^{j} \right)}^{H}{A_{i}\left( {\overset{\rightarrow}{x}}^{i} \right)}}} \right)} = 0_{N \times N}} & (3) \end{matrix}$

The condition of Equation (3) indicates that ML decoding can be performed on symbols belonging to one group independent of symbols belonging to another group when x_(i) ₁ , x_(i) ₂ , . . . , x_(i) _(L) (i_(l)∈{1,2, . . . ,N}, l=1,2, . . . ,L) symbols associated with the matrix A_(i)({right arrow over (x)}^(i)) are grouped into the one group.

In a transmitter for encoding data into quasi-orthogonal STBCs and transmitting the quasi-orthogonal STBCs, one codeword matrix G({right arrow over (x)}) is generated when one arbitrary N-dimensional input vector {right arrow over (x)} is input, and columns of the codeword matrix G({right arrow over (x)}) are transmitted through different transmit antennas.

It is assumed that a channel between each transmit antenna and each receive antenna is an independent Rayleigh fading channel. Moreover, it is assumed that the channel is a quasi-static channel in which a channel value is not varied while one codeword matrix is transmitted. When a complex low-pass equivalent reception signal received from the m-th receive antenna during the t-th time interval is denoted by r_(l,m), a reception vector {right arrow over (r)}_(m) received during N symbol periods is given as shown in Equation (4). $\begin{matrix} {{\overset{\quad\rightarrow}{r}}_{m} = {\left\lbrack {r_{1,m},\ldots\quad,r_{N,m}} \right\rbrack^{T} = {{\frac{1}{\sqrt{N}}G{\overset{\rightarrow}{h}}_{m}} + {\overset{\rightarrow}{n}}_{m}}}} & (4) \end{matrix}$

In Equation (4), a channel vector {right arrow over (h)}_(m)=[h_(l,m), . . . ,h_(N,m)]^(T) and the (n,m)-th channel value h_(n,m)=h_(n,m) ^(I)+jh_(n,m) ^(Q) is an independent and identical distributed (i.i.d.) complex channel gain between the n-th transmit antenna and the m-th receive antenna, where h_(n,m) ^(I) and h_(n,m) ^(Q) are i.i.d. Gaussian random variables with a mean value of 0 and a variance value of 0.5. Further, {right arrow over (n)}_(m)=[n_(n,m), . . . ,n_(N,m)]^(T) and n_(t,m)=n_(t,m) ^(I)+jn_(t,m) ^(Q) denote the contribution of background thermal noise modeled by i.i.d. random variables in r_(t,m), where n_(t,m) ^(I) and n_(t,m) ^(Q) are Gaussian random variables with a mean value of 0 and a variance value of N₀/2. A codeword matrix is normalized to $\frac{1}{\sqrt{N}}$ such that total transmission power is equal to that of a non-coding system, not using STBCs.

When complex conjugates are taken for rows of the reception vector {right arrow over (r)}_(m) associated with indices of rows configured only by complex linear combinations of x₁*,x₂*, . . . ,x_(N)* in the codeword matrix G({right arrow over (x)}), an equivalent reception vector {right arrow over (y)}_(m) is generated. The equivalent reception vector {right arrow over (y)}_(m) can be expressed as shown in Equation (5) based on an input vector {right arrow over (x)}. {right arrow over (y)}=H _(m) {right arrow over (x)}+{right arrow over (n)}′ _(m)   (5)

In Equation (5), elements of a channel matrix H_(m) are complex linear combinations of $\frac{h_{1,m}}{\sqrt{N}},\ldots\quad,\frac{h_{N,m}}{\sqrt{N}},\frac{h_{1,m}^{*}}{\sqrt{N}},\ldots\quad,{\frac{h_{N,m}^{*}}{\sqrt{N}}.}$ Here, {right arrow over (n)}′_(m)=[n′_(m,1), . . . ,n′_(m,N)]^(T) denotes a noise vector obtained by taking complex conjugates of rows of {right arrow over (n)}_(m) associated with indices of rows in which complex conjugates are taken for the reception vector {right arrow over (r)}_(m) in order to generate the equivalent reception vector {right arrow over (y)}_(m). The statistical characteristics of {right arrow over (n)}′_(m) are the same as those of {right arrow over (n)}_(m).

Under an assumption that the channel matrix H_(m) is known, the receiving stage can perform ML decoding and select an N-dimensional input vector {circumflex over ({right arrow over (x)})} as shown in Equation (6). $\begin{matrix} \begin{matrix} {\overset{\bigwedge\limits^{\rightarrow}}{x} = {\arg\quad{\min\limits_{\overset{\quad\rightarrow}{x}}{\sum\limits_{m = 1}^{M}{{{\overset{\rightarrow}{y}}_{m} - {\frac{1}{\sqrt{N}}{G\left( \overset{\rightarrow}{x} \right)}{\overset{\rightarrow}{h}}_{m}}}}^{2}}}}} \\ {= {\arg\quad{\min\limits_{\overset{\quad\rightarrow}{x}}{\sum\limits_{m = 1}^{M}\left\lbrack {{- \frac{1}{\sqrt{N}}}{\sum\limits_{i = 1}^{N}\left( {{{\overset{\rightarrow}{y}}_{m}^{H}{G_{i}\left( x_{i} \right)}{\overset{\rightarrow}{h}}_{m}} +} \right.}} \right.}}}} \\ \left. {\left. {~~}{{\overset{\quad\rightarrow}{h}}_{\quad m}^{\quad H}\quad{\quad{G_{\quad i}\left( \quad x_{\quad i} \right)}}^{H}\quad{\quad\overset{\quad\rightarrow}{y}}_{\quad m}} \right) + {\frac{1}{N}{{\overset{\rightarrow}{h}}_{m}^{H}\left( {\sum\limits_{i = 1}^{P}{A_{i}\left( {\overset{\rightarrow}{x}}^{i} \right)}^{H}} \right)}\left( {\sum\limits_{i = 1}^{P}{A_{i}\left( {\overset{\rightarrow}{x}}^{i} \right)}} \right){\overset{\rightarrow}{h}}_{m}}} \right\rbrack \\ {= {\arg\quad{\min\limits_{\overset{\quad\rightarrow}{x}}{\sum\limits_{m\quad = \quad 1}^{M}\left\lbrack {{- \frac{1}{\sqrt{N}}}\quad{\sum\limits_{i\quad = \quad 1}^{N}\left( {{{\overset{\quad\rightarrow}{y}\quad}_{m}^{H}\quad{G_{i}\left( x_{i} \right)}\quad{\overset{\quad\rightarrow}{h}\quad}_{m}}\quad +}\quad \right.}} \right.}}}} \\ \left. {\left. {{\overset{\quad\rightarrow}{h}\quad}_{m}^{\quad H}\quad{\quad{G_{\quad i}\left( \quad x_{\quad i} \right)}}^{H}\quad{\quad\overset{\quad\rightarrow}{y}\quad}_{m}} \right) + {\frac{1}{N}{{\overset{\rightarrow}{h}}_{m}^{H}\left( {\sum\limits_{i = 1}^{P}{{A_{i}\left( {\overset{\rightarrow}{x}}^{i} \right)}^{H}{A_{i}\left( {\overset{\rightarrow}{x}}^{i} \right)}}} \right)}{\overset{\quad\rightarrow}{h}\quad}_{m}}} \right\rbrack \end{matrix} & (6) \end{matrix}$

In Equation (6), ∥ ∥ denotes a Frobenius norm value. Equation (6) is divided into P Equations. As shown in Equation (7), of the P Equations, an L-dimensional subvector {circumflex over ({right arrow over (x)})}^(i) can be selected. $\begin{matrix} {{\overset{\bigwedge\limits^{\rightarrow}}{x}}^{i} = {\arg\quad{\min\limits_{\quad^{\quad{\overset{\rightarrow}{x}}^{i}}}{\sum\limits_{m = 1}^{M}\left\lbrack {{\frac{1}{N}{\overset{\quad\rightarrow}{h}\quad}_{m}^{\quad H}{A_{i}\left( {\overset{\rightarrow}{x}}^{i} \right)}^{H}{A_{i}\left( {\overset{\rightarrow}{x}}^{i} \right)}{\overset{\quad\rightarrow}{h}\quad}_{m}} - {\frac{1}{\sqrt{N}}{\sum\limits_{j = 1}^{L}\left( {{{\overset{\quad\rightarrow}{y}\quad}_{m}^{H}\quad{G_{i_{j}}\left( x_{i} \right)}\quad{\overset{\quad\rightarrow}{h}\quad}_{m}}\quad + {{\overset{\quad\rightarrow}{h}\quad}_{m}^{\quad H}\quad{\quad{G_{\quad i_{j}}\left( \quad x_{\quad i} \right)}}^{H}\quad{\quad\overset{\quad\rightarrow}{y}\quad}_{m}}} \right)}}} \right\rbrack}}}} & (7) \end{matrix}$

When the ML decoding method is used, the ML decoding can be performed on each of the P L-dimensional sub-input vectors {right arrow over (x)}^(i).

The channel matched filter 20 multiplies the equivalent reception vector {right arrow over (y)}_(m) by the complex conjugate transpose matrix H_(m) ^(H) of the channel matrix H_(m), and generates a channel matched filtered vector {right arrow over (y)}m,mat as shown in Equation (8). {right arrow over (y)} _(m,mat) =H _(m) ^(H) {right arrow over (y)} _(m)=(H _(m) ^(H) H _(m)){right arrow over (x)}+H _(m) ^(H) {right arrow over (n)}′ _(m)   (8)

FIG. 2 illustrates details of the grouping unit 30 of FIG. 1. The grouping unit 30 includes a first extraction module 33 for extracting signals from each of the channel matched filtered vectors {right arrow over (y)}_(m,mat) output by the channel matched filters in a unit of L signals such that the signals do not overlap with each other, and a plurality of grouping modules 35 for grouping the L signals extracted from the first extraction module 33 and generating the P L-dimensional sub-channel matched filtered vectors {right arrow over (y)}_(m,mat) ^(i). The grouping unit 30 groups elements y_(m,mat,i) _(I) , . . . ,y_(m,mat) _(L) of a channel matched filtered vector {right arrow over (y)}_(m,mat) associated with indices i_(I), . . . ,i_(L) of symbols within an L-dimensional sub-input vector {right arrow over (x)}^(i), and generates L-dimensional sub-channel matched filtered vectors {right arrow over (y)}_(m,mat).

The channel matrix H_(m) can be written as shown in Equation (9). H_(m)[{right arrow over (H)}_(m,I), . . . ,{right arrow over (H)}_(m,N)]  (9)

Here, {right arrow over (H)}_(m,n) denotes the n-th N-dimensional column vector of the channel matrix H_(m).

When column vectors associated with indices i₁, . . . ,i_(L) in the channel matrix H_(m) are grouped, an N×L sub-channel matrix H_(m) ^(i) as shown in Equation (10) can be generated. H_(m) ^(i)=[{right arrow over (H)}_(m,i) _(I) , . . . ,{right arrow over (H)}_(m,i) _(L) ]  (10)

When elements associated with indices i₁, . . . ,i_(L) in the noise vector {right arrow over (n)}′_(m) are grouped, a sub-noise vector is defined as ({right arrow over (n)}′_(m))^(i)=[n′_(m,i) _(I) , . . . ,n′_(m,i) _(L) ]^(T).

The sub-channel matched filtered vectors {right arrow over (y)}_(m,mat) ^(i) generated by the grouping unit 30 can be expressed as shown in Equation (11) due to quasi-orthogonal characteristics of the quasi-orthogonal STBCs. {right arrow over (y)} _(m,mat) ^(i) =R _(m) ^(i) {right arrow over (x)} ^(i) ′{right arrow over (v)} _(m) ^(i)   (11)

In Equation (11), R_(m) ^(i)=(H_(m) ^(i))^(H) H_(m) ^(i) denotes an L×L sub correlation matrix, and {right arrow over (v)}_(m) ^(i)=(H_(m) ^(i))^(H)({right arrow over (n)}′_(m))^(i) denotes a channel matched filtered sub-noise vector.

An arbitrary element y_(m,mat) ^(i) within the sub-channel matched filtered vector {right arrow over (y)}_(m,mat) ^(i) includes only components x_(i) ₁ ,x_(i) ₂ , . . . , x_(i) _(L) of the input symbols, and (L−1) symbols x_(i) ₁ , . . . , x_(i) _(i-1) , x_(i) _(i+1) , . . . , x_(i) _(L) except a symbol x_(i) _(I) serves as an interference to x_(i) ^(I).

FIG. 3 is a block diagram illustrating details of the combiner 40. The combiner 40 includes a plurality of second extraction modules 43 for extracting vectors from the P sub-channel matched filtered vectors {right arrow over (y)}_(m,mat) ^(i) output by each of the plurality of grouping units one by one. The combiner 40 also includes a plurality of combination modules 45 for combining M vectors extracted from the plurality of second extraction modules 43 and generating the P L-dimensional sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i). The combiner 40 adds sub-channel matched filtered vectors {right arrow over (y)}_(m,mat) ^(i) corresponding to the i-th output vectors of the grouping units and outputs sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i) as shown in Equation (12). $\begin{matrix} {{\overset{\quad\rightarrow}{y}\quad}_{mat}^{i} = {{\sum\limits_{m = 1}^{M}{\overset{\quad\rightarrow}{y}\quad}_{m,{mat}}^{i}} = {{R\overset{i\rightarrow i}{x}} + {\overset{\rightarrow}{v}}^{i}}}} & (12) \end{matrix}$

In Equation (12), $R^{i} = \left( {\sum\limits_{m = 1}^{M}R_{m}^{i}} \right)$ is an L×L sub-equivalent correlation matrix, and ${\overset{->}{v}}^{i} = {\sum\limits_{m = 1}^{M}{\overset{->}{v}}_{m}^{i}}$ is an L -dimensional sub-equivalent noise vector.

FIG. 4 is a block diagram illustrating details of the interference cancellation decoder 50. The interference cancellation decoder performs iterative interference cancellation on sub-channel matched filtered vectors {right arrow over (y)}_(mat) ^(i) I times and generates estimation vectors {right arrow over (x)}_(k) _(I) ^(i,(I)) for sub-input vectors {right arrow over (x)}^(i). The interference cancellation decoder performs ML decoding on the estimation vectors and demodulates the sub-input vectors {right arrow over (x)}^(i).

For a given modulation order Q, a set of Q constellation symbols is defined as S={s₁,s₂, . . . ,s_(Q)}. A set of (L−1)-dimensional constellation symbol vectors is defined as W={[w₁, . . . W_(L−1)]^(T)|w_(i)∈S}. The number of candidates for an arbitrary symbol x_(i) _(I) ∈S is Q. The number of possible candidates for a (L−1)-dimensional symbol vector {right arrow over (z)}_(i) _(I) =[x_(i) _(I) , . . . ,x_(i) _(i-1) , x_(i) _(i+1) , . . . ,x_(i) _(L) ∈W except for x_(i) _(I) is Q^(L−1).

The (L−1)-dimensional symbol vector {right arrow over (z)}_(I) ^(i) except the symbol x_(i) _(I) associated with one arbitrary element y_(mat,I) ^(i) within the sub-equivalent channel matched filtered vector {right arrow over (y)}_(mat) ^(i) serves as an interference symbol vector to the symbol x_(i) _(I) , and arbitrary vectors serving as candidates of an initial interference symbol vector can be selected from the set W.

For example, all Q^(L−1) vectors belonging to the set W can be selected as candidates of an interference symbol vector {right arrow over (z)}_(I) ^(i)=[x_(i) ₂ , . . . ,x_(i) _(L) ]^(T), except the symbol x_(i) _(I) associated with y_(mat,I) ^(i). Alternatively, K_(I)(≦Q^(L−1)) candidates closest to the sub-equivalent channel matched filtered vector {right arrow over (y)}_(mat) ^(i) can be selected from all the Q^(L−1) candidates, and only candidates present within a predetermined distance from the sub-equivalent channel matched filtered vector {right arrow over (y)}_(mat) ^(i) can be selected.

Because the symbols x_(i) ₂ , . . . , x_(i) _(L) in the element y_(mat,I) ^(i) serve as interference to the symbol x_(i) _(I) , an interference component associated with each candidate of the interference symbol vector {right arrow over (z)}_(I) ^(i) in the element y_(mat,I) ^(i) is eliminated as shown in Equation (13), such that y_(mat,I,k) _(I) ^(i,(I)) is generated. $\begin{matrix} {y_{{mat},1,k_{1}}^{i,{(1)}} = {y_{{mat},1}^{i} - {\sum\limits_{j \neq 1}^{L}{\left( R^{i} \right)_{1,j}z_{1,k_{1},j}^{i,{(1)}}}}}} & (13) \end{matrix}$

The superscript b of z_(l,k) _(b) _(,j) ^(i(b)) denotes an index in the current interference cancellation step, and z_(l,k) _(b) _(,j) ^(i,(b)) denotes the j-th element of {right arrow over (z)}_(l,k) _(b) ^(i,(b)) serving as the k_(b)-th candidate of the interference symbol vector {right arrow over (z)}_(l) ^(i) in the b-th interference cancellation step. (R^(i))_(l,j) denotes the (l,j)-th element of the sub-equivalent correlation matrix R^(i), and y_(mat,l,k) _(b) ^(i,(b)) denotes a value of a signal from which an interference component has been eliminated, associated with the k_(b)-th interference symbol vector candidate in the l-th element y_(mat,l) ^(i) of the sub-channel matched filtered vector {right arrow over (y)}_(mat) ^(i). The number of candidates of the (L−1)-dimensional interference symbol vector {right arrow over (z)}_(l) ^(i) is defined as K_(b). Accordingly, k_(l) denotes indices of candidates of the interference symbol vector {right arrow over (z)}_(l) ^(i) serving as interference to x_(i) ₁ in the first interference cancellation step. When all the vectors belonging to the set W are selected as candidates of {right arrow over (z)}₁ ^(i), the number of candidates of {right arrow over (z)}₁ ^(i) is Q^(L−1).

In the first interference cancellation step, the k₁-th interference symbol vector candidate {right arrow over (z)}_(1,k) _(I) ^(i,(I)) determines the symbol x_(i) ₁ from a signal y_(mat,l,k) _(I) ^(i,(I)) from which interference has been eliminated. In this case, a determined value is referred to as x_(i) _(I) _(,k) _(I) ^((I)). Then, K₁ candidate symbols associated with the symbol x_(i) ₁ are generated in the first interference cancellation step, and K₁ estimation vectors {right arrow over (x)}_(k) _(I) ^(i,(I)) for the sub-input vectors {right arrow over (x)}^(i) can be obtained as shown in Equation (14). {right arrow over (x)}_(k) ₁ ^(i,(I))=[x_(i) ₁ _(,k) ₁ ⁽¹⁾,x_(i) ₂ _(,k) ₁ ⁽⁰⁾,x_(i) ₃ _(,k) ₁ ⁽⁰⁾, . . . ,x_(i) _(L) _(,k) ₁ ⁽⁰⁾]^(T)   (14)

In Equation (14), a number included in the superscript ( ) denotes an interference cancellation step index. Here, x_(i) ₂ _(,k) ₁ ⁽⁰⁾, . . . ,x_(i) _(L) _(,k) ₁ ⁽⁰⁾ denote symbols with a vector associated with the k₁-th candidate of the interference symbol vector {right arrow over (z)}₁ ^(i) before the initial interference cancellation step.

An (L−1)-dimensional interference symbol vector {right arrow over (z)}₂ ^(i) in which the i₂-th symbol is excluded from the K_(I) estimation vectors {right arrow over (x)}_(k) _(I) ^(i,(1)) has K_(I) candidates {right arrow over (z)}_(2,k) _(I) ^(i,(2))=[x_(i) ₁ _(,k) ₁ ⁽¹⁾,x_(i) ₃ _(,k) ₁ ⁽⁰⁾,x_(i) ₄ _(,k) ₁ ⁽⁰⁾, . . . ,x_(i) _(L) _(,k) ₁ ⁽⁰⁾]^(T). Because (L−1)-dimensional interference symbol vector candidates are vectors generated by removing one element from L-dimensional estimation vector candidates, the same interference symbol vector candidates for different estimation vector candidates may be generated. In this case, only different interference symbol vector candidates are selected. One method for selecting different candidates selects an index k₂ in which Equation (15) is satisfied from the K₁ interference symbol vector candidates. Candidates of {right arrow over (z)}₂ ^(i) associated with the selected index k₂ are denoted by {right arrow over (z)}_(2,k) ₂ ^(i,(2)), and the number of different candidates is defined as K₂ (K₂≦K₁). k ₂∈{1,w|{right arrow over (z)} _(2,w) ^(i,(2)) ≠{right arrow over (z)} _(2,u) ^(i,(2)),^(∀) u,1≦u≦w≦K ₁}  (15)

Because the symbols x_(i) ₁ ,x_(i) ₃ , . . . ,x_(i) _(L) in the element y_(mat,2) ^(i) in the second interference cancellation step serve as an interference to the symbol x_(i) ₂ , an interference component associated with each candidate of the interference symbol vector {right arrow over (z)}₂ ^(i) is eliminated as shown in Equation (16), such that y_(mat,2,k) ₂ ^(i,(2)) is generated. $\begin{matrix} {y_{{mat},2,k_{2}}^{i,{(2)}} = {y_{{mat},2}^{i} - {\sum\limits_{j \neq 2}^{L}{\left( R^{i} \right)_{2,j}z_{2,k_{2},j}^{i,{(2)}}}}}} & (16) \end{matrix}$

In Equation (16), (R^(i))_(2,j) denotes the (2,j)-th element of the sub correlation matrix R^(i), and z_(2,k) ₂ _(,j) ^(i,(2)), denotes the j-th element of the interference symbol vector {right arrow over (z)}_(2,k) ₂ ^(i(2)).

In the second interference cancellation step, the k₂-th interference symbol vector candidate {right arrow over (z)}_(2,k) ₂ ^(i(2)) determines the symbol x_(i) ₂ from a signal y_(mat,2,k) ₂ ^(i,(2)) from which interference has been eliminated. In this case, a determined value is referred to as x_(i) ₂ _(,k) ₂ ⁽²⁾. Then, K₂ candidate symbols associated with the symbol x_(i) ₂ are generated in the second interference cancellation step, and K₂ estimation vectors {right arrow over (x)}_(k) ₂ ^(i,(2))=[x_(i) ₁ _(,k) ₂ ⁽¹⁾,x_(i) ₂ _(,k) ₂ ⁽²⁾,x_(i) ₃ _(,k) ₂ ⁽⁰⁾, . . . ,x_(i) _(L) _(,k) ₂ ⁽⁰⁾]^(T) for the sub-input vectors {right arrow over (x)}^(i) can be obtained.

An (L−1)-dimensional interference symbol vector {right arrow over (z)}₃ ^(i) in which the i₃-th symbol is excluded from the K₂ estimation vectors {right arrow over (x)}_(k) ₂ ^(i,(2)) has K₂ candidates {right arrow over (z)}_(3,k) ₂ ^(i,(3))=[x_(i) ₁ _(,k) ₂ ⁽¹⁾,x_(i) ₂ _(,k) ₂ ⁽²⁾,x_(i) ₄ _(,k) ₂ ⁽⁰⁾, . . . x_(i) _(L) _(,k) ₂ ⁽⁰⁾]^(T). To select different interference symbol vector candidates, an index is selected using Equation (15) and the selected index is referred to as k₃. Candidates of the interference symbol vector {right arrow over (z)}₃ ^(i) are {right arrow over (z)}_(3,k) ₃ ^(i,(2))=[x_(i) ₁ _(,k) ₃ ⁽¹⁾,x_(i) ₂ _(,k) ₃ ⁽²⁾,x_(i) ₄ _(,k) ₃ ⁽⁰⁾, . . . ,x_(i) _(L) _(,k) ₃ ⁽⁰⁾]^(T), and K₃ (K₃≦K₂) candidates are generated.

When the interference cancellation process is continuously performed L times, K_(L) (K_(L)≦ . . . ≦K₁) candidate symbols associated with the symbol x_(i) _(L) are generated from y_(mat,L) ^(i), and K_(L) (K_(L)≦K_(L−1)) estimation vector candidates {right arrow over (x)}_(k) ₂ ^(i,(L))=[x_(i) ₁ _(,k) ₂ ⁽¹⁾, . . . ,x_(i) _(L−1) _(,k) ₂ ^((L−1)),x_(i) _(L) _(,k) _(L) ^((L))]^(T) for the sub-input vectors {right arrow over (x)}^(i) can be obtained. Furthermore, K_(L+1) (K_(L+1)≦K_(L)) different candidates {right arrow over (z)}_(1,k) _(L) ^(i,(L+1))=[x_(i) ₂ _(,k) _(L) ⁽²⁾, . . . ,x_(i) _(L−1) _(,k) ₂ ^((L−1)),x_(i) _(L) _(,k) _(L) ^((L))]^(T) can be obtained for the interference symbol vector {right arrow over (z)}₁ ^(i) associated with the K_(L) estimation vector candidates {right arrow over (x)}_(k) _(L) ^(i,(L)). Interference components associated with K_(L+1) different candidates {right arrow over (x)}_(k) _(L) ^(i,(L+1)) of the interference symbol vector {right arrow over (z)}_(I) ^(i) are removed from y_(mat,I) ^(i) and the symbol x_(i) _(I) can be re-determined.

After the interference cancellation is continuously performed I times, K_(I) estimation candidate vectors {right arrow over (x)}_(k) _(I) ^(i,(I)) for the sub-input vectors {right arrow over (x)}^(i) can be obtained. This case can reduce the number of estimation candidate vectors as compared with one interference cancellation operation.

As shown in FIG. 4, an ML decoder 55 performs ML decoding on K_(I) different estimation candidate vectors and demodulates L-dimensional sub-input vectors {right arrow over (x)}^(i). Accordingly, the inventive ML decoding method can reduce decoding complexity as compared with the conventional ML decoding method.

In accordance with the present invention, an interference canceller 53 generates K₂ different estimation vectors {right arrow over (x)}_(k) ₂ ^(i,(2)) after performing the interference cancellation twice, and selects estimation vector candidates associated with an index k₂ in which a condition of x_(i) ₂ _(,k) ₁ ⁽⁰⁾=x_(i) ₂ _(,k) ₂ ⁽²⁾ is satisfied. The ML decoding is performed on the selected estimation vector candidates, such that the L-dimensional sub-input vectors {right arrow over (x)}^(i) can be demodulated. Accordingly, decoding complexity can be reduced.

In accordance with the present invention, the decoding apparatus includes an interference canceller and an ML decoder that are connected to each other, such that a gain for reducing decoding complexity can be obtained even when arbitrary transmit antennas are used in quasi-orthogonal STBCs.

In accordance with the present invention, the decoding method uses an iterative interference cancellation and ML decoding scheme, such that it can reduce decoding complexity without sudden performance loss as compared with the ML decoding method.

Although preferred embodiments of the present invention have been disclosed for illustrative purposes, those skilled in the art will appreciate that various modifications, additions, and substitutions are possible, without departing from the scope of the present invention. Therefore, the present invention is not limited to the above-described embodiments, but is defined by the following claims, along with their full scope of equivalents. 

1. An apparatus for receiving and decoding quasi-orthogonal space-time block codes (STBCs) from a transmitter for encoding data into the quasi-orthogonal STBCs and transmitting the STBCs using a plurality of transmit antennas, comprising: a plurality of channel matched filters for performing channel matched filtering on M N-dimensional equivalent reception vectors {right arrow over (y)}_(m) (m=1, . . . ,M) received through M receive antennas and outputting N-dimensional channel matched filtered vectors {right arrow over (y)}_(m,mat) (m=1, . . . ,M); a plurality of grouping units for generating P L-dimensional sub-channel matched filtered vectors {right arrow over (y)}_(m,mat) ^(i) (i=1, . . . ,P, m=1, . . . ,M) from each of the N-dimensional channel matched filtered vectors {right arrow over (y)}_(m,mat); a combiner for generating P L-dimensional sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i) (i=1, . . . ,P) using the sub-channel matched filtered vectors {right arrow over (y)}_(m,mat) ^(i); and an interference cancellation decoder for performing iterative interference cancellation and maximum likelihood (ML) decoding on each of the L-dimensional sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i), and demodulating P L-dimensional sub-input vectors {right arrow over (x)}^(i) (i=1, . . . ,P).
 2. The apparatus of claim 1, wherein each of the plurality of grouping units comprises: a first extraction module for extracting signals from each of the channel matched filtered vectors {right arrow over (y)}_(m,mat) output by the channel matched filters in a unit of L signals such that the signals do not overlap with each other; and a plurality of grouping modules for grouping the L signals extracted from the first extraction module and generating the P L-dimensional sub-channel matched filtered vectors {right arrow over (y)}_(m,mat) ^(i).
 3. The apparatus of claim 1, wherein the combiner comprises: a plurality of second extraction modules for extracting vectors from the P sub-channel matched filtered vectors {right arrow over (y)}_(m,mat) ^(i) output by each of the plurality of grouping units one by one; and a plurality of combination modules for combining M vectors extracted from the plurality of second extraction modules and generating the P L-dimensional sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i).
 4. The apparatus of claim 1, wherein the interference cancellation decoder comprises: an interference canceller for performing iterative interference cancellation on each of the sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i) I times and generating K_(I) different estimation candidate vectors {right arrow over (x)}_(k) _(I) ^(i(I))(i=1, . . . ,P) for the L-dimensional sub-input vectors {right arrow over (x)}_(i); and an ML decoder for performing ML decoding on the estimation candidate vectors {right arrow over (x)}_(k) _(I) ^(i(I)) and demodulating the P L-dimensional sub-input vectors {right arrow over (x)}^(i).
 5. The apparatus of claim 1, wherein the sub-input vectors {right arrow over (x)}^(i) are demodulated from the sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i), respectively.
 6. The apparatus of claim 4, wherein the interference canceller eliminates interference from a plurality of candidate vectors of an interference symbol vector configured by (L−1) symbols from which a symbol x_(i) _(I) associated with one arbitrary element y_(m,mat,I) ^(i) within the sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i) is excluded, and generates a plurality of subvectors from which the interference has been eliminated.
 7. The apparatus of claim 6, wherein the interference canceller selects an arbitrary number of vectors, serving as candidate vectors of initial interference symbol vectors before performing interference cancellation, from all (L−1)-dimensional symbol vectors from which a symbol x_(i) _(I) associated with one arbitrary element y_(mat,I) ^(i) within the sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i) is excluded.
 8. The apparatus of claim 7, wherein the interference canceller selects K₁ (K₁≦Q^(L−1)) arbitrary candidates of all Q^(L−1) candidates for the (L−1)-dimensional symbol vectors closest to the sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i) from the candidate vectors of the initial interference symbol vectors.
 9. The apparatus of claim 7, wherein the interference canceller selects K₁ (K₁≦Q^(L−1)) candidates of the candidate vectors of the initial interference symbol vectors present in a predetermined distance from the sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i).
 10. The apparatus of claim 4, wherein the interference canceller determines symbols x_(i) _(I) from the sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i) from which interference has been eliminated to generate the estimation candidate vectors {right arrow over (x)}_(k) _(I) ^(i,(I)), and combines values of the determined symbols x_(i) _(I) and (L−1)-dimensional interference symbol vectors associated therewith.
 11. The apparatus of claim 4, wherein the interference canceller performs iterative interference cancellation to reduce the number of estimation candidate vectors to be generated after eliminating interference from the sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i).
 12. The apparatus of claim 4, wherein the interference canceller generates the K_(I) different estimation candidate vectors {right arrow over (x)}_(k) _(I) ^(i,(I)) that satisfy a condition of K₁≦K_(I−1)≦ . . . ≦K_(I) after performing iterative interference cancellation on the sub-equivalent channel matched filtered vectors {right arrow over (y)}_(mat) ^(i) I times.
 13. The apparatus of claim 12, wherein the interference canceller selects new estimation candidate vectors by selecting only vectors that are different from the estimation candidate vectors {right arrow over (x)}_(k) _(I) ^(i,(I)) generated after performing the interference cancellation in a method for determining the estimation candidate vectors {right arrow over (x)}_(k) _(I) ^(i,(I) m)after performing the interference cancellation.
 14. The apparatus of claim 12, wherein the interference canceller performs the iterative interference cancellation, such that the number of different estimation candidate vectors {right arrow over (x)}_(k) _(I) ^(i,(I)) is gradually reduced.
 15. The apparatus of claim 4, wherein the interference canceller generates K₂ different estimation candidate vectors {right arrow over (x)}_(k) ₂ ^(i,(2)) after performing two interference cancellation steps, and selects estimation vectors associated with an index k₂ in which a condition of x_(i) ₂ _(,k) ₁ ⁽⁰⁾=x_(i) ₂ _(,k) ₂ ⁽²⁾ is satisfied from the K₂ different estimation candidate vectors {right arrow over (x)}_(k) ₂ ^(i,(2)).
 16. The apparatus of claim 15, wherein the ML decoder performs ML decoding on the estimation vectors associated with the index k₂ in which the condition of x_(i) ₂ _(,k) ₁ ⁽⁰⁾=x_(i) ₂ _(,k) ₂ ⁽²⁾ m is satisfied, and demodulates the L-dimensional sub-input vectors {right arrow over (x)}^(i).
 17. The apparatus of claim 4, wherein the ML decoder performs the ML decoding on the K_(I) estimation candidate vectors {right arrow over (x)}_(k) _(I) ^(i,(I)) generated from the interference canceller, and demodulates the L-dimensional sub-input vectors {right arrow over (x)}^(i). 